A triple construction for Lie bialgebras

Grabowski, Jan (2005) A triple construction for Lie bialgebras. Pacific Journal of Mathematics, 221 (2). pp. 281-301. ISSN 0030-8730

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Abstract

We study the triple of a quasitriangular Lie bialgebra as a natural extension of the Drinfel’d double. The triple is itself a quasitriangular Lie bialgebra. We prove several results about the triple’s algebraic structure, analogous to known results for the Drinfel’d double: among them, that in the factorisable case the triple is isomorphic to a twisting of g ⊕ g ⊕ g by a certain cocycle. We also consider real forms of the triple and the triangular case.